What does Acts 23:32 mean?

Lysias, the Roman tribune, had a mess on his hands. A strange man, Paul, came to Jerusalem about a week prior. Everyone in the city seems to want him dead (Acts 21:31; 23:10). And yet, not only has he not committed a crime, he's a Roman citizen (Acts 22:25). Lysias needs to discover why everyone wants him dead while keeping him safe. When the Jewish religious leaders make a pact with forty determined men to assassinate Paul (Acts 23:12–15), Lysias gives up. He can't keep Paul in custody without a reason, but he can't let him go or he'll be killed. So, he sends Paul to the governor and tells the religious leaders to go to Caesarea Maritima and give their charges (Acts 23:30).

Lysias wants to make sure his prisoner stays safe in the journey from Jerusalem to Caesarea—particularly the first leg to Antipatris. So two hundred soldiers, two hundred spearmen, seventy horsemen, and two centurions leave with Paul three hours after sunset and march the thirty miles through the night (Acts 23:23). The territory from Antipatris to Caesarea is in Samaria and has far fewer Jews. The soldiers aren't worried about an ambush on this leg, so the infantrymen and spearmen return to Jerusalem while the horsemen continue with Paul.

The "barracks" are the Antonia Fortress, the tall building rising next to the northwest corner of the temple mount, and the smaller buildings to the east. It is the headquarters for six hundred Roman peace-keeping forces; Herod the Great built it and named it after Mark Antony.